In this paper two cosmological models representing the flat Friedmann universe filled with a Chaplygin fluid, with or without dust, are analyzed in terms of the recently proposed “statefinder” parameters. Trajectories of both models in the parameter plane are shown to be significantly different with respect to the “quiessence” and “tracker” models. The generalized Chaplygin gas model with an equation of state of the form $p=-A/{\rho }^{\alpha }$ is also analyzed in terms of the statefinder parameters.

We study the role that tachyon fields may play in cosmology as compared to the well-established use of minimally coupled scalar fields. We first elaborate on a kind of correspondence existing between tachyons and minimally coupled scalar fields; corresponding theories give rise to the same cosmological evolution for a particular choice of the initial conditions but not for any other. This leads us to study a specific one-parameter family of tachyonic models based on a perfect fluid mixed with a positive cosmological constant. For positive values of the parameter, one needs to modify Sen’s action and use the $\sigma$ process of resolution of singularities. The physics described by this model is dramatically different and much richer than that of the corresponding scalar field. For particular choices of the initial conditions, the universe, which does mimic for a long time a de Sitter–like expansion, ends up in a finite time in a special type of singularity that we call a big brake. This singularity is characterized by an infinite deceleration.

We present a study of quantum scalar fields on de Sitter (dS) space-time based on analyticity in the complexified Riemannian manifold; a new expansion of the linear fields in terms of coordinate independent dS plane waves and an explicit form of the propagators at real or imaginary times are given. Our approach controls the thermal properties and the zero-curvature limit of the fields; it provides a general setting for interacting fields, in which some steps are taken: a Källen-Lehmann type formula for complete propagators and a treatment of a class of self-energy diagrams and their resummation.

We propose a general framework for quantum field theory on the de Sitter space-time (i.e. for local field theories whose truncated Wightman functions are not required to vanish). By requiring that the fields satisfy a weak spectral condition, formulated in terms of the analytic continuation properties of their Wightman functions, we show that a geodesical observer will detect in the corresponding “vacuum” a blackbody radiation at temperature T =1/2 πR. We also prove the analogues of the PCT, Reeh-Schlieder and Bisognano-Wichmann theorems.